Suppose we have two rooms A and B that are the same size and connected by an open doorway, so the air has the same pressure and volume in both rooms. This means that $P_AV_A = P_BV_B$ and $n_AT_A = n_BT_B$. If room A is warmer than room B then $n_A < n_B$ so room B contains the greater mass of air.
I understand it from the equations but I want to be able to imagine it. Is it because the energy that comes from the sun increase the mean kinetic energy in the room that is closer to the sun and that results in higher probability of molecules moving into the other room in long enough period of time?